Use of software tools to support education and training is widespread. Computer Algebra Systems (CAS) such as Mathematica, Maple and Matlab for the same are also very common, particularly in mathematics and engineering. In this study, a symbolic view of stability and sensitivity of some basic computational procedures are given using Mathematica. Several Mathematica notebooks are prepared and used in an introductory numerical computing course to support the lectures. As it was demonstrated, Mathematicaís symbolic power may be quite effective, to discuss rather abstract concepts of stability and sensitivity by allowing students to experience these issues in a laboratory environment without bothering about the intricate steps of the analysis.